Recovery of 3-D closed surfaces using progressive shell models

This paper is concerned with the problems of reconstructing a closed surface from scattered, noisy 3-D data. A progressive shell model is a 3-D extension of the 2-D progressive contour model. We employ finite element methods (FEMs) to reduce the number of the required variables and improve the efficiency in storage and computation. The fundamental forms in differential geometry are used to measure rigid-motion invariant properties and formulate the internal energy of the shell. We also develop a wireframe model associated with a subdivision scheme to overcome the difficulty of generating a smooth boundary between two adjacent patches. This is a direct application of the 2-D contour model where curve segments or wires are used instead of patches. In the subdivision scheme, we impose the co-plane constraints to determine a unique normal vector at the interpolated mid-point. To demonstrate the descriptive ability of a wireframe model, we conduct experiments on 3-D data set of a tumor and a face.